Can we screen a funny video about our teacher?
Your comic masterpiece could get you into legal trouble. If your teacher (or his lawyer) gets the bright idea that you've damaged his reputation, he could sue you for "defamation" or "libel." To win, he would need to show that you made statements that were untrue and that caused others to think less of him. He won't have much trouble proving that he was the subject of the video, since you used his name! There are certain defenses your lawyer might present in court, but let's make sure you don't end up in court at all.
It's not easy to determine whether your video violates defamation and libel laws. For example, you might think it was a compliment to represent your teacher with a plastic action figure. But I'll bet your teacher's lawyer argues that his new plastic self comes off as "stiff" and "inflexible." Then again, proving that one's reputation has been damaged is not easy either. If your video doesn't lower the opinion that people already have of your teacher, he's got an uphill battle. (It would be even harder if he were already a "public figure" -- which is why shows like Saturday Night Live don't get sued once a week.)
Here's how the professional moviemakers deal with this type of dilemma: They either get a signed "release" from the person who is the subject of the film or they have an attorney review the film before it's shown publicly. By signing a "release," your teacher would be consenting to the use of his name or image. Of course, if your teacher is incensed by the video, he won't be inclined to sign anything you send his way -- other than a transfer out of his class. You can find standard form releases in Nolo's book Getting Permission: How to License & Clear Copyrighted Materials Online & Off, by Richard Stim.
You could run into another problem if your video is successful and generates money. Your teacher could sue you for using his name for a commercial purpose, under "right of publicity" laws. Again, however, if you can talk your teacher into signing a release, you'll be protected.